Theorems · Definition · field theory
Subfield.gi
(K : Type u) → [inst : DivisionRing K] → GaloisInsertion Subfield.closure SetLike.coe
closure forms a Galois insertion with the coercion to set.
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement and proof · cited by 303
- Subfield.closurestatement and proof · cited by 39
- GaloisInsertionstatement · cited by 35
- Subfield.closure_leproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Subfield.closure_eqproof · cited by 4
- Subfield.closure_unionproof · cited by 2
- Subfield.closure_sUnionproof · cited by 1
- RingHom.map_field_closureproof · cited by 1
- Subfield.closure_emptyproof · cited by 0
- Subfield.closure_iUnionproof · cited by 0